Error propagation

Angular closure of a seven-sided traverse against a k√n tolerance

Seven interior angles that sum 21 seconds over the geometric condition. Test the misclosure against the k√n tolerance a 10-second instrument justifies, then distribute it equally and prove the adjusted angles close.

Recall· about 18 minutes by hand· 4 steps

Given

  • A closed seven-sided traverse was observed with a 10″ total station, each interior angle turned by one direct and one reverse pointing and meaned.
  • Observed interior angles, in station order:
  • 1: 128°14′22″ 2: 96°37′48″ 3: 142°05′11″ 4: 118°49′36″
  • 5: 154°22′07″ 6: 131°58′44″ 7: 127°52′33″
  • The field specification allows an angular misclosure of k√n seconds, with k taken as the least count of the instrument, 10″, and n the number of angles.
  • No angle is suspected of a blunder; all were turned with the same procedure and the same care.

Required

  • The geometric condition the seven angles must satisfy, and the observed misclosure.
  • Whether the misclosure meets the tolerance.
  • The correction to each angle and the adjusted angles.

Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.

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